Game Development Reference
nition suppliers. More often, they provide ballistic tables of downrange heights. It is
important when using these charts that you remember they assume the scope to be
horizontal and that the bullet starts with a negative height below the scope line.
Table 18-1 shows data from Remington's website and assumes the rifle was zeroed at
100 yards; it tells you how far the bullet is below the horizontal at every 50 yards past
that 0. You can tune the drag coefficient in the projectile simulation to match these
Table 18-1. Long-range trajectory Remington Express .45-70 Govt
Range in yards
Drop in inches
From this table you can see that the bullet drop is over two feet at 250 yards. This means
that if the target is at 250 yards and your scope is zeroed at 100 yards, then you would
have to aim two feet above your target to hit it. That might be high enough that you
can't even see the target in the scope anymore!
To counteract this problem, most rifles come with scopes that have elevation adjust‐
ments. This is a knob on the side of the scope that can be rotated to discrete settings
called clicks. Most scopes use a 1/4 minute of angle adjustment per click although some
use 1/8, 1/2, or even full minutes. A minute of angle is simply 1/60 of a degree. Therefore,
when adjusting for elevation, the shooter can turn a knob on the scope, and as she hears
the clicks, she knows that she has adjusted her scope however many minutes of angle.
Now when she re-aims the crosshairs on the target, the barrel will have a slightly different
angle than it did before, essentially aiming higher to accommodate the longer distance.
To achieve high accuracy in the field, the shooter would know that she zeroed her rifle
to a certain range. Then, when attempting a shot, she would estimate the range to her
target and adjust the scope however many clicks up or down. The biggest cause of error
is an inaccurate estimate of range. Modern shooters often use laser range finders to
determine exactly what elevation offset is required. In long-distance shooting situations,
you can provide the range to the users and let them adjust the rifle's scope from the
current zero range to a new zero range.
Most games today don't model even the effect of gravity on a bullet, so adding elevation
adjustment to a sniper or hunting portion of your game will add much-needed accuracy.
Just like in the Chapter 6 projectile example, our target shooting game's bullets are
affected by wind. Just as before, a bullet's susceptibility to wind largely depends on its
lateral drag coefficient. In our simulation, you can tune the bullet's susceptibility to the
wind by adjusting the factor Cw . This, again, will apply only to rifles shooting at long
ranges. At 20 meters, the wind will have little to do in determining where a bullet will
hit. At 600 meters, it can cause the bullet to be off by a meter! The adjustment for wind